W1. (a) Calculate x , A. D., o, and om for the first set of data containing ten time intervals (not the reaction times). Employ the appropriate formulas and show all of the steps in your calculations. Compare your calculated values to the values that you obtained from the computer. Compute the percentage differences and comment. (b) Compare the value of om, of the reaction times obtained by your group to the corresponding value of om for the interval times. Is there any special relationship (e.g. a relatively small value of o in one data set that is comparable to the value of om, for the other data set)? Should there be such a property? Explain your reasoning. What does a large or small value of om indicate? List the values that you checked in order to answer this question. W2. (a) What fraction of the ten measurements in the first set of ten values fall in the interval x to? What fractions of the measurements lie in the range x +20 and in the range x 130 ? Write down the actual ranges of the intervals that you checked. Are these values compatible with those predicted by the Gaussian Distribution? Denote the individual data values within the ranges that you compared. Compute the percentage difference of your values from the theoretical values. Are the percentage difference values reasonable? Explain the results and show all of your calculations. (b) Using a table, indicate those data points that fell outside of the ranges. W3. (a) Answer Questions W1 and W2 for the whole set of thirty data points (instead of just the sets of ten data points analyzed previously). Which set, the thirty-point data set or ten-point data set, came closer to the expected values? 7(b) If you used Excel to find x and o for all of the thirty points, you will have entered a formula such as =StDev(Range). What range did you use for this thirty-point data set (e.g. for W1, your range might have been A1:A10)? W4. (a) Determine whether the average of the second set falls within plus or minus one Standard Deviation of the mean from the average value of the first set and again within two and three om . Show the range of the values that you checked for this question. (b) Why do we check the range of om, in Part (a) instead of the range of o ? What is its significance? What does it mean if it falls within 30,, of x of the first set? Give an approximate value for the percentage that they are in agreement. W5. (a) At first it seems odd that when you increase the number of measurements from ten to thirty, o does not change much, but om, becomes smaller. Does this trend hold for your data? Quote your numerical results in your response. (b) What do the formulas indicate? Write down the equations and explain. (c) What are the physical significances of SD (o ) and SDmean (Om )? What do they represent? (d) Why is one smaller than the other? W6. From your current data for the interval (all thirty points), you have a certain percentage uncertainty for the Average that would be (m/x) . 100%. If you wanted to reduce the percentage uncertainty by 1/3, how many measurements would you need to take? Show all of your calculations. The results will indicate why good survey data in politics, medical trials, marketing, et cetera can be very expensive.9/21/2021 14:54 Reaction Times 1 0.547483 0.059814 2 0.300774 0.312735 3 0.374227 0.296657 4 9.12E-02 0.33968 5 0.640102 0.301973 Intervals 2.125 1.999 1.906 2.187 2.015 2.062 2.094 1.999 2.046 YOUIDWNY 1.999 1.968 2.015 2.016 2.015 1.999 2.015 1.984 2.093 2.094 1.999 2.047 8 2.015 2.031 1.999 9 1.968 2 1.968 10 2.015 1.984 2.047 Answers AVE SD SDMean set #1 React Times 0.390764 0.214953 0.09613 set #2 React Times 0.262172 0.114331 0.05113 set #1 Intervals 2.0528 0.068592 0.021691 set #2 intervals 1.9994 0.018094 0.005722 set #3 intervals 2.0182 0.053543 0.016932 Total 30 2.023467 0.054382 0.009929 1.969084 2.077849
